Examples of Rational Inequalities

Procedure for Solving Rational Inequalities

In a corporate safety audit, a technician uses the inequality $\frac{250}{p - 15} \leq 25$ to model pressure limits in a storage tank. When solving any inequality of this type where a variable appears in the denominator, which of the following is a fundamental rule that must be recalled regarding the values that make the denominator zero?

An operations analyst is reviewing the mathematical foundations for analyzing cost-to-volume ratios, such as the inequality $\frac{1000}{x - 5} \leq 200$. To ensure accurate modeling, match each term below with its correct rule or definition as it applies to rational inequalities.

A logistics analyst uses the inequality $\frac{500}{d} \leq 25$ to model the relationship between fuel consumption and distance $d$. Because this inequality contains a rational expression with the variable in the denominator, it is specifically classified as a(n) ____ inequality.

A warehouse manager is using a rational inequality to determine the most cost-effective inventory level while staying within budget constraints. To solve the inequality correctly and find the valid range of values, the manager must follow a standard logical procedure. Arrange the following steps for solving a rational inequality in the correct order.

Sign Reversal in Rational Inequalities

When a logistics coordinator uses a rational inequality such as $\frac{100}{x} \leq 5$ to analyze shipping rates, any values of $x$ that make the denominator equal to zero must be excluded from the final solution set because division by zero is undefined.